A covering second-order Lagrangian for the relativistic top without forces. (English) Zbl 1092.70017

Matsyuk, Roman Ya.

Nikitin, A.G. (ed.) et al., Proceedings of the fourth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, July 9–15, 2001. Part 2. Dedicated to the 200th anniversary of M. Ostrohrads’kyi. Kyïv: Institute of Mathematics of NAS of Ukraine (ISBN 966-02-2486-9). Proc. Inst. Math. Natl. Acad. Sci. Ukr., Math. Appl. 43(2), 741-745 (2002).

The author derives a fourth-order differential equation allowing for the complete elimination of spin variables from Dixon’s equations of motion of a relativistic top. A parameter-homogeneous covariant Lagrangian of second order is considered which covers the case of free relativistic top at constraint manifold of constant acceleration.
For the entire collection see [Zbl 0989.00035].

Reviewer: N. M. Ivanova (Kyïv)

MSC:

70H40	Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
70H03	Lagrange’s equations
70E17	Motion of a rigid body with a fixed point

Keywords:

Dixon equation; Hamilton-Ostrogradskii approach